System and methods to model bridging and fluid diversion

Abstract

Systems and methods presented herein relate to techniques for modeling bridging and fluid diversion and generating a bridging volume output and / or fluid diversion output that indicates a bridging occurrence and / or operations to remedy the bridging. For example, a method includes utilizing a physics based empirical model to predict fluid diversion away from a constriction of a fluid diverter system based on an injection rate, concentration of diverter material, particulate type ratios of particulate types in the fluid diverter system, carrier fluid rheology, or a combination thereof. The method also includes generating an output based on the predicted fluid diversion.

Description

SYSTEM AND METHODS TO MODEL BRIDGING AND FLUID DIVERSIONCROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims priority to and the benefit of U.S. Provisional Patent Application Serial No. 63 / 595,796, entitled “Systems and Methods to Model Bridging and Fluid Diversion,” filed November 3, 2023, which is hereby incorporated by reference in its entirety for all purposes.BACKGROUND

[0002] The present disclosure generally relates to systems and methods for generating a bridging volume output and / or fluid diversion output.

[0003] This section is intended to introduce the reader to various aspects of art that may be related to various aspects of the present techniques, which are described and / or claimed below. This discussion is believed to be helpful in providing the reader with background information to facilitate a better understanding of the various aspects of the present disclosure. Accordingly, it should be understood that these statements are to be read in this light, and not as an admission of any kind.

[0004] It may be appreciated that stimulation diversion processes and systems have been in use for years. Typically, stimulation diversion processes and systems are comprised of downhole production logging tools (PLT), radioactive tracers with gamma ray detection tools and fiber optic strings measuring distributed temperature. These measurements in the PLT usually have single pressure, single flow meter, gamma ray and temperature. The data fromthese downhole tools are real time when an electric cable and / or fiber optic fiber is connected inside the coiled tubing string, or in memory mode when the data is collected after the job.

[0005] Stimulation diversion processes are remarkably complex. One process that occurs during stimulation diversion processes is bridging. During bridging, a wellbore obstruction forms due to a buildup of material such as scale, wellbore fill, or cuttings. In some instances, bridging may be desirable. For example, it may be desirable to have bridging for certain materials occur in a relatively controlled manner for a portion (e.g., <100%) of restrictions. Moreover, at least in some instances, it may be advantageous that at least some bridging occurs. Such bridging materials may improve the effectiveness of the stimulation treatment and hence improve production. However, some types of bridging, such as bridging due to scale, wellbore fill, and the like, may be detrimental to the production of fluids, and thus are desirable to avoid.SUMMARY

[0006] A summary of certain embodiments described herein is set forth below. It should be understood that these aspects are presented merely to provide the reader with a brief summary of these certain embodiments and that these aspects are not intended to limit the scope of this disclosure.

[0007] Certain embodiments of the present disclosure include a method. The method includes utilizing a physics based empirical model to predict fluid diversion away from one or more constrictions of a fluid diverter system disposed within a wellbore based on an injection rate, concentration of diverter material, particulate type ratios of particulate types in the fluiddiverter system, carrier fluid rheology, or a combination thereof. The method also includes generating an output based on the predicted fluid diversion.

[0008] Certain embodiments of the present disclosure include a system. The system includes a control system comprising one or more processors. The control system is configured to determine one or more bridging volumes formed within a wellbore. The control system is also configured to adjust one or more model parameters of a model based on the one or more bridging volumes, wherein the model represents a fluid diverter system based on an injection rate, concentration of diverter material, particulate type ratios of particulate types in the fluid diverter system, carrier fluid rheology, or a combination thereof, and wherein the model is stored in a storage component that is accessible by the control system. Further, the control system is configured to generate a bridging volume output based on the one or more adjusted model parameters.

[0009] Certain embodiments of the present disclosure include a method. The method includes determining one or more bridging volumes with a wellbore perforation. The method also includes adjusting one or more model parameters of a model based on the one or more bridging volumes, wherein the model represents a fluid diverter system based on an injection rate, concentration of diverter material, particulate type ratios of particulate types in the fluid diverter system, carrier fluid rheology, or a combination thereof. Further, the method includes generating a bridging volume output based on the one or more adjusted model parameters.

[0010] Various refinements of the features noted above may be undertaken in relation to various aspects of the present disclosure. Further features may also be incorporated in these various aspects as well. These refinements and additional features may exist individually or inany combination. For instance, various features discussed below in relation to one or more of the illustrated embodiments may be incorporated into any of the above-described aspects of the present disclosure alone or in any combination. The brief summary presented above is intended to familiarize the reader with certain aspects and contexts of embodiments of the present disclosure without limitation to the claimed subject matter.BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Various aspects of this disclosure may be better understood upon reading the following detailed description and upon reference to the drawings, in which:

[0012] FIGS. 1 and 2 are schematic illustrations of an oilfield well that traverses a hydraulically-fractured hydrocarbon-bearing reservoir as well as a downhole well tool for milling out plugs that isolate a number of intervals offset from one another along the length of the well, in accordance with embodiments of the present disclosure;

[0013] FIG. 3 is a schematic illustration of a well system that obtains sensor data to dynamically update information related to operation and control of a downhole well tool, in accordance with embodiments of the present disclosure;

[0014] FIG. 4 illustrates a well control system that may include a surface processing system to control the well system described herein, in accordance with embodiments of the present disclosure;

[0015] FIG. 5 illustrates a schematic diagram of a first example of a model system that may be used to determine a bridging volume, in accordance with embodiments of the present disclosure;

[0016] FIG. 6 illustrates a schematic diagram of a second example of a model system that may be used to determine a bridging volume, in accordance with embodiments of the present disclosure;

[0017] FIG. 7 illustrates a flow diagram for generating a bridging volume output, in accordance with embodiments of the present disclosure;

[0018] FIG. 8 is an image showing a perspective view of an example of the model system for determining a bridging volume corresponding to a plug accumulation, in accordance with embodiments of the present disclosure; and

[0019] FIG. 9 shows a schematic diagram of perforations and a bridging volume blocking the perforations, in accordance with an embodiment of the present disclosure.DETAILED DESCRIPTION

[0020] One or more specific embodiments of the present disclosure will be described below. These described embodiments are only examples of the presently disclosed techniques.Additionally, in an effort to provide a concise description of these embodiments, all features of an actual implementation may not be described in the specification. It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions must be made to achieve the developers’ specific goals, such as compliance with system-related and business-related constraints, whichmay vary from one implementation to another. Moreover, it should be appreciated that such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure.

[0021] When introducing elements of various embodiments of the present disclosure, the articles “a,” “an,” and “the” are intended to mean that there are one or more of the elements. The terms “comprising,” “including,” and “having” are intended to be inclusive and mean that there may be additional elements other than the listed elements. Additionally, it should be understood that references to “one embodiment” or “an embodiment” of the present disclosure are not intended to be interpreted as excluding the existence of additional embodiments that also incorporate the recited features.

[0022] As used herein, the terms “connect,” “connection,” “connected,” “in connection with,” and “connecting” are used to mean “in direct connection with” or “in connection with via one or more elements”; and the term “set” is used to mean “one element” or “more than one element.” Further, the terms “couple,” “coupling,” “coupled,” “coupled together,” and “coupled with” are used to mean “directly coupled together” or “coupled together via one or more elements.” As used herein, the terms “up” and “down,” “uphole” and “downhole”, “upper” and “lower,” “top” and “bottom,” and other like terms indicating relative positions to a given point or element are utilized to more clearly describe some elements. Commonly, these terms relate to a reference point as the surface from which drilling operations are initiated as being the top (e.g., uphole or upper) point and the total depth along the drilling axis being the lowest (e.g., downhole or lower) point, whether the well (e.g., wellbore, borehole) is vertical, horizontal or slanted relative to the surface.

[0023] As used herein, a fracture shall be understood as one or more cracks or surfaces of breakage within rock. Fractures can enhance permeability of rocks greatly by connecting pores together and, for that reason, fractures can be induced mechanically in some reservoirs in order to boost hydrocarbon flow. Certain fractures may also be referred to as natural fractures to distinguish them from fractures induced as part of a reservoir stimulation. Fractures can also be grouped into fracture clusters (or “perf clusters”) where the fractures of a given fracture cluster (perf cluster) connect to the wellbore through a single perforated zone. As used herein, the term “fracturing” refers to the process and methods of breaking down a geological formation and creating a fracture (i.e., the rock formation around a well bore) by pumping fluid at relatively high pressures (e.g., pressure above the determined closure pressure of the formation) in order to increase production rates from a hydrocarbon reservoir.

[0024] In addition, as used herein, the terms “real time”, ’’real-time”, or “substantially real time” may be used interchangeably and are intended to described operations (e.g., computing operations) that are performed without any human-perceivable interruption between operations. For example, as used herein, data relating to the systems described herein may be collected, transmitted, and / or used in control computations in “substantially real time” such that data readings, data transfers, and / or data processing steps occur once every second, once every 0.1 second, once every 0.01 second, or even more frequent, during operations of the systems (e.g., while the systems are operating). In addition, as used herein, the terms “automatic” and “automated” are intended to describe operations that are performed are caused to be performed, for example, by a processing system (i.e., solely by the processing system, without human intervention).

[0025] Diversion refers to a phenomenon triggering significant changes in the treatment fluids reservoir-injectivity profile during the treatment pumping. The goal of diversion is to ensure that all reservoir zones of interest receive a sufficient amount of treatment fluids.Diverting fluids away from an initially high-injectivity zone may require some choking of the flow to that zone, such that initially lower-injectivity ones may see an additional flux of treatment fluids. In the context of this paper, choking is achieved by accumulating some permeable solid material, or filter cake (e.g., a plug), at the flow entrance of the target zone, its perforations. The idea of choking perforations flow, with a permeable material, to promote diversion has been used widely in the field with different systems, including rock salts, wax beads, crushed carbonate.

[0026] Accordingly, the present disclosure relates to techniques for generating a bridging volume output and / or a fluid diversion output using a diversion empirical model (e.g., a physics based model, a diversion model). In general, the techniques include developing a diversion empirical model that may be utilized in fracturing and acidizing applications in perforated wells. As noted herein, it may be advantageous for bridging to occur in some instances, while in other instances it may be desirable to avoid bridging. The techniques described herein may be applied to both types of bridging (e.g., desirable or undesirable). For example, the disclosed techniques may be applied to bridging during injection of stimulation and other well treatments for improving production of injection in the well. The diversion empirical model may store relationships related to a likelihood of fluid diversion away from a constriction based on injection rate, concentration of the diversion material, particular types (e.g., particulate size, particulate shape), ratios of particulate types present in and / or near a constriction, carrier fluid rheology, or a combination thereof. As referred to here, the “constriction” is generally a regionwhere a flow of fluid rate decreases, such as a perforation, a wormhole, an induced fracture, a natural fracture, a flow control valve, an intelligent completion device, other downhole valves, or other completion elements where a fluid may flow through, such as a packer. The diversion empirical model may include an empirical particular bridging model and a skin model. In some instances, the skin model may be used in conjunction with existing models. Moreover, the disclosed models may utilize calibration parameters that may provide a more accurate prediction of fluid diversion away from the constriction. In any case, the present techniques also include determining one or more model parameters of the diversion empirical model using experimental laboratory data or field data. In some embodiments, the techniques include determining an occurrence of diversion (e.g., in real-time, such as in the field).

[0027] It should be noted that the present techniques may be used in applications that where solid particulates may accumulate. For example, the present techniques may be used in applications that include solid particulates that may form plugs (e.g., permeable filter cakes) inside perforations. One technique that may be utilized to achieve diversion with particulates is to control and predict particulates bridging in the perforations such that perforation plugging can start. Modeling this physical process is challenging as it depends on, for example, wellbore dynamics at the time of particles aggregation including parameters such as injection rate, diverter system fluid formulation, concentration of diverter material, size of particulates, size of perforation and so on. Today, no reliable model can predict the volume utilized for particulates flowing through a perforation to bridge, with realistic fluid-particulates systems in realistic flow conditions.

[0028] Further, although the above description is directed to hydraulic fracturing applications, it should be noted that the disclosed techniques for diversion may be applied toapplications involving downhole chemical treatments injected into a reservoir. Such applications include, but are not limited to, matrix acidizing, sand control, scale prevent on / removal, water control / shut off, water injection for enhanced oil recovery (EOR), polymer and surfactant flooding for EOR, and steam injection for EOR.

[0029] With the foregoing in mind, FIGS. 1 and 2 are schematic illustrations of an example well system 10 that has undergone perforation and fracturing applications. As illustrated, in certain embodiments, a platform and derrick 12 may be positioned over a wellbore 14 that traverses a hydrocarbon-bearing reservoir 16 by rotary drilling. While certain elements of the well system 10 are illustrated in FIGS. 1 and 2, other elements of the well (e.g., blow-out preventers, wellhead “tree”, etc.) have been omitted for clarity of illustration. In certain embodiments, the well system 10 includes an interconnection of pipes, including vertical and horizontal casing 18, tubing 20 (e.g., coiled tubing), transition 22, and a production liner 24 that connect to a surface facility (as illustrated in FIG. 3) at the surface 26 of the well system 10. In certain embodiments, the tubing 20 extends inside the casing 18 and terminates at a tubing head (not shown) at or near the surface 26. In addition, in certain embodiments, the casing 18 contacts the wellbore 14 and terminates at a casing head (not shown) at or near the surface 26. In certain embodiments, the production liner 24 and / or the horizontal casing 18 have aligned radial openings termed “perforation zones” 28 that allow fluid communication between the production liner 24 and the hydraulically fractured hydrocarbon-bearing reservoir or formation 16.

[0030] In certain embodiments, a number of plugs 30 may be disposed in the well system 10 at positions offset from one another along the longitudinal length of the wellbore 14 in order to provide hydraulic isolation between certain intervals of the well system 10 with a number ofperforation zones 28 in each interval. In certain embodiments, each plug 30 may include one or more expanding slips and seal members for anchoring and sealing the plug 30 to the production liner 24 or the casing 18. In addition, in certain embodiments, each plug 30 may be formed primarily from composite materials (or other suitable materials) that enables the plug 30 to be milled-out for removal as described in greater detail herein.

[0031] In certain embodiments, a bottom hole assembly (“BHA”) 32 may be run inside the casing 18 by the tubing 20 (which may be coiled tubing or drill pipe). As illustrated in FIG. 2, in certain embodiments, the BHA 32 may include a downhole motor 34 that operates to rotate a milling tool 36. In certain embodiments, the downhole motor 34 may be driven by hydraulic forces carried in milling fluid supplied from the surface 26 of the well system 10. In certain embodiments, the BHA 32 may be connected to the tubing 20, which is used to run the BHA 32 to a desired location within the wellbore 14. It is also contemplated that, in certain embodiments, the rotary motion of the milling tool 36 may be driven by rotation of the tubing 20 effectuated by a rotary table or other surface-located rotary actuator. In such embodiments, the downhole motor 34 may be omitted.

[0032] In certain embodiments, the tubing 20 may also be used to deliver milling fluid (arrows 38) to the milling tool 36 to aid in the milling process and carry cuttings and possibly other fluid and solid components in fluid 40 (referred to herein as “return fluid”) that flows up the annulus between the tubing 20 and the casing 18 (or via a return flow path provided by the tubing 20, in certain embodiments) for return to the surface facility (as illustrated in FIG. 3). In certain embodiments, the BHA 32 may be located such that the milling tool 36 is positioned in direct contact with a plug 30. In such embodiments, the rotary motion of the milling tool 36 mills away the plug 30 into cuttings that flow as part of the return fluid 40 that is returned to thesurface facility (as illustrated in FIG. 3). It is also contemplated that the return fluid 40 may include remnant proppant (e.g., sand) or possibly rock fragments that result from the hydraulic fracturing application, and flow within the well system 10 during the plug mill-out process. After the plug 30 is removed by the milling, a flow path is opened past the drill plug. Under certain conditions, fracturing fluid and possibly hydrocarbons (oil and / or gas), proppants and possibly rock fragments may flow from the fractured reservoir 16 through the perforations 28 in the newly opened interval and back to the surface 26 of the well system 10 as part of the return fluid 40. In certain embodiments, the BHA 32 may be supplemented behind the rotary drill by an isolation device such as, for example, an inflatable packer that may be activated to isolate the zone below or above it, and enable local pressure tests.

[0033] FIG. 3 is a schematic illustration of the well system 10 of FIGS. 1 and 2. As illustrated in FIG. 3, in certain embodiments, the well system 10 may include a downhole well tool 42 that is moved along the wellbore 14 via coiled tubing 20. In certain embodiments, the downhole well tool 42 may include a variety of drilling / cutting tools coupled with the coiled tubing 20 to provide a coiled tubing string 44. In the illustrated embodiment, the downhole well tool 42 includes a milling tool 36, which may be powered by a motor 34 (e.g., a positive displacement motor (PDM), or other hydraulic motor). In certain embodiments, the milling tool 36 may be used to mill out a plug 30 or plugs 30 disposed along the wellbore 14. Although described primarily herein as relating to embodiments for milling out plugs 30, in other embodiments, other type of milling targets may be milled out, such as cement, obstructions along the wellbore 14, naturally occurring obstructions such as deposits from formation fluid or injected fluid, objects left in the wellbore 14 from previous operations, warped or deformed completion tubulars, and so forth. In certain embodiments, the wellbore 14 may be an openwellbore or a cased wellbore defined by a casing 18. As described herein, in certain embodiments, the wellbore 14 may be vertical or horizontal or inclined. It should be noted the downhole well tool 42 may be part of various types of BHAs 32 coupled to the coiled tubing 20. In certain embodiments, the plug(s) 30 may be disposed along the wellbore 14 within a downhole completion.

[0034] Particularly, in certain embodiments, the plug(s) 30 may be disposed along a horizontal section of the wellbore 14. Once delivered in place, such plug(s) 30 may be anchored and sealed against the casing 18. Once anchored and sealed, perforation may be applied above the plug 30 through the casing 18, as illustrated in FIG. 2. The perforation application may be followed by hydraulic applications to direct high pressure fracturing fluid through the casing perforations 28 into the adjacent formation 16, to cause fracturing of reservoir rock for easier production. Typical hydraulic fracturing fluid may contain other substances such as proppant, sand, fiber, etc., to keep the fractures open after the completion of hydraulic fracturing. The placement, anchoring, perforation, and fracturing process may be repeated by moving from downhole to uphole interval by interval, until the entire formation and production zone are treated as designed.

[0035] Upon completion and treatment, such plugs 30 may be removed before producing the well. In general, removal of such plugs 30 may include milling out operations, usually by coiled tubing 20. To improve the efficacy of plug mill-outs, in certain embodiments, the well system 10 also may include a downhole sensor package 46 having a plurality of downhole sensors 48. In certain embodiments, the sensor package 46 may be mounted along the coiled tubing string 44, although certain downhole sensors 48 may be positioned at other downhole locations in other embodiments. In certain embodiments, data from the downhole sensors 48may be relayed uphole to a surface processing system 50 (e.g., a computer-based processing system) disposed at the surface 26 and / or other suitable location of the well system 10.

[0036] In certain embodiments, the data may be relayed uphole in substantially real time (e g., relayed while it is detected by the downhole sensors 48 during operation of the downhole well tool 42) via a wired or wireless telemetric control line 52, and this real-time data may be referred to as edge data. For example, in certain embodiments, during a milling operation, the real-time data may be in the form of torque data (e.g., torque applied by the downhole hydraulic motor 34) and thrust data (e.g., weight on bit with respect to a milling bit). In certain embodiments, the torque data and thrust data may be combined to establish torque-thrust curves that, in turn, may be used to determine various parameters related to certain plugs 30 or other targets and / or operation of the milling tool 36. In certain embodiments, the telemetric control line 52 may be in the form of an electrical line, fiber-optic line, or other suitable control line for transmitting data signals. In certain embodiments, the telemetric control line 52 may be routed along an interior of the coiled tubing 20, within a wall of the coiled tubing 20, or along an exterior of the coiled tubing 20. In addition, as described in greater detail herein, additional data (e.g., surface data) may be supplied by surface sensors 54 and / or stored in memory locations 56. By way of example, historical data and other useful data may be stored in a memory location 56 such as cloud storage 58.

[0037] As illustrated, in certain embodiments, the coiled tubing 20 may deployed by a coiled tubing unit 60 and delivered downhole via an injector head 62. In certain embodiments, the injector head 62 may be controlled to slack off or pick up on the coiled tubing 20 so as to control the tubing string weight and, thus, the weight on bit (WOB) acting on the bit of the milling tool36 (or other downhole well tool 42).

[0038] In certain embodiments, fluid 38 may be delivered downhole under pressure from a pump unit 64. In certain embodiments, the fluid 38 may be delivered by the pump unit 64 through the downhole hydraulic motor 34 to power the downhole hydraulic motor 34 and, thus, the milling tool 36. In certain embodiments, the fluid 40 is returned uphole, and this flow back of fluid is controlled by suitable flowback equipment 66. In certain embodiments, the flowback equipment 66 may include chokes and other components / equipment used to control flow back of the return fluid 40 in a variety of applications, including well treatment applications.

[0039] In certain embodiments, the downhole well tool 42 may be moved along the wellbore 14 via the coiled tubing 20 under control of the injector head 62 so as to apply a desired tubing weight and, thus, to achieve a desired rate of penetration (ROP) as the milling tool 36 is operated to mill through the plugs 30. In certain embodiments, the controlled movement of the well tool 42 via the coiled tubing 20 may be used in a variety of applications other than milling out plugs 30. Depending on the specifics of a given application, various types of data may be collected downhole, and transmitted to the surface processing system 50 in substantially real time to facilitate improved operation of the downhole well tool 42. For example, the data may be used to fully or partially automate the downhole operation, to optimize the downhole operation, and / or to provide more accurate predictions regarding components or aspects of the downhole operation.

[0040] As described in greater detail herein, the pump unit 64 and the flowback equipment 66 may include advanced sensors, actuators, and local controllers, such as PLCs, which may cooperate together to provide sensor data to, receive control signals from, and generate local control signals based on communications with, respectively, the surface processing system 50. In certain embodiments, as described in greater detail herein, the sensors may include flow rate,pressure, and fluid rheology sensors, among other types of sensors. In addition, as described in greater detail herein, the actuators may include actuators for pump and choke control of the pump unit 64 and the flowback equipment 66, respectively, among other types of actuators.

[0041] FIG. 4 illustrates a well control system 68 that may include the surface processing system 50 to control the well system 10 described herein. In certain embodiments, the surface processing system 50 may include one or more analysis modules 70 (e.g., a program of computer-executable instructions and associated data) that may be configured to perform various functions of the embodiments described herein. In certain embodiments, to perform these various functions, an analysis module 70 executes on one or more processors 72 of the surface processing system 50, which may be connected to one or more storage media 74 of the surface processing system 50. Indeed, in certain embodiments, the one or more analysis modules 70 may be stored in the one or more storage media 74.

[0042] In certain embodiments, the one or more processors 72 may include a microprocessor, a microcontroller, a processor module or subsystem, a programmable integrated circuit, a programmable gate array, a digital signal processor (DSP), or another control or computing device. In certain embodiments, the one or more storage media 74 may be implemented as one or more non-transitory computer-readable or machine-readable storage media. In certain embodiments, the one or more storage media 74 may include one or more different forms of memory including semiconductor memory devices such as dynamic or static random access memories (DRAMs or SRAMs), erasable and programmable read-only memories (EPROMs), electrically erasable and programmable read-only memories (EEPROMs) and flash memories; magnetic disks such as fixed, floppy and removable disks; other magnetic media including tape; optical media such as compact disks (CDs) or digital video disks (DVDs); or other types ofstorage devices. Note that the computer-executable instructions and associated data of the analysis module(s) 70 may be provided on one computer-readable or machine-readable storage medium of the storage media 74, or alternatively, may be provided on multiple computer- readable or machine-readable storage media distributed in a large system having possibly plural nodes. Such computer-readable or machine-readable storage medium or media are considered to be part of an article (or article of manufacture), which may refer to any manufactured single component or multiple components. In certain embodiments, the one or more storage media 74 may be located either in the machine running the machine-readable instructions, or may be located at a remote site from which machine-readable instructions may be downloaded over a network for execution.

[0043] In certain embodiments, the processor(s) 72 may be connected to a network interface 76 of the surface processing system 50 to allow the surface processing system 50 to communicate with the various downhole sensors 48 and surface sensors 54 described herein, as well as communicate with the actuators 78 and / or PLCs 80 of the surface equipment 82 (e.g., the coiled tubing unit 60, the pump unit 64, the flowback equipment 66, and so forth) and of the downhole equipment 84 (e.g., the BHA 32, the downhole motor 34, the milling tool 36, the downhole well tool 42, and so forth) for the purpose of controlling operation of the well system 10, as described in greater detail herein. In certain embodiments, the network interface 76 may also facilitate the surface processing system 50 to communicate data to cloud storage 58 (or other wired and / or wireless communication network) to, for example, archive the data or to enable external computing systems 86 to access the data and / or to remotely interact with the surface processing system 50.

[0044] It should be appreciated that the well control system 68 illustrated in FIG. 4 is only one example of a well control system, and that the well control system 68 may have more or fewer components than shown, may combine additional components not depicted in the embodiment of FIG. 4, and / or the well control system 68 may have a different configuration or arrangement of the components depicted in FIG. 4. In addition, the various components illustrated in FIG. 4 may be implemented in hardware, software, or a combination of both hardware and software, including one or more signal processing and / or application specific integrated circuits. Furthermore, the operations of the well control system 68 as described herein may be implemented by running one or more functional modules in an information processing apparatus such as application specific chips, such as application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), programmable logic devices (PLDs), systems on a chip (SOCs), or other appropriate devices. These modules, combinations of these modules, and / or their combination with hardware are all included within the scope of the embodiments described herein.

[0045] FIG. 5 illustrates a schematic diagram of a first example of a model system 88 that may be used to determine a bridging volume, in accordance with embodiments of the present disclosure. In general, the schematic diagram illustrates a conduit having a constriction. As referred to herein, a “bridge” refers to a wellbore obstruction caused by a buildup of material such as scale, wellbore fill, or cuttings that can restrict wellbore access or, in severe cases, eventually close the wellbore. A “bridging volume” refers to a volume or amount of the bridge. As shown, fluid flows from the chamber (e.g., having a pressure Pu) to the constriction (e.g., having a pressure Pd). After some injection of fluid, a plug or bridge forms, thereby causing the pressure Pu to increase (e.g., corresponding to the positive slope on the graph).

[0046] FIG. 6 illustrates a schematic diagram of a second example of a model system 100 that may be used to determine a bridging volume, in accordance with embodiments of the present disclosure. In this case, the model system 100 includes two perforations where a bridge or plug may form. The graph shows a decrease in qperf, which corresponds to an occurrence of bridging, thereby preventing fluid from flowing along the perforations. In general, the model system 100 shown in FIG. 6 may be used to measure a bridging volume on multiple constrictions with a predetermined time period, or simultaneously. In general operation of the model system 88 and / or model system 100, particulate-laden fluid is injected through a chamber and the fluid can only exit through constrictions (e.g., the perforations).

[0047] The size of the constriction experimentally models the conduit through which bridging is to be achieved and determined (e.g., a casing perforation, a fracture). Two nonlimiting example flow conditions of the particulate-laden fluid through the constrictions are described below. For example, in a first example, the total injection rate is imposed and constant. In a second example, the injection pressure is imposed and constant. In either example, the flowrate through each constriction is measured. To determine bridging, based on the conditions of example 1, the pressure-drop Ap between an upstream and downstream position across each constriction is monitored during injection. To determine bridging, based on the conditions of example 2, the measured flowrate through each constriction may be used. To determine a bridging occurrence, for example, techniques include determining an increase (e.g., a sudden increase) in the pressure drop indicates that bridging has occurred for the constriction under consideration, the monitored volume or mass of particulates injected at that point is the bridging volume of the constriction in consideration. For example 1 with multiple constriction and example 2: A sudden drop in the constriction flowrate qPerf indicates that bridging hasoccurred for the constriction under consideration, the monitored volume or mass of particulates injected at that point is the bridging volume of the constriction in consideration.

[0048] In any case (e.g., example flow conditions), the techniques described above may be repeated by varying experimental parameters such as injection rates, constriction size, particulates concentration, particulates shapes (e.g., isotropic, anisotropic), proportions of particulates types (shape, size), carrier fluid properties and determine their effect on the bridging volume.

[0049] From the above experimental observations, empirical particulate bridging volume models can be developed. An example of such model is detailed in Eq. (l)-(4) in S.I. units. Refinement of this model can be achieved by performing additional experiments.8 = (3) tipIn some embodiments, a may be a function of the driving force for bridging. In this study, a appears to be a function of t / perf. An empirical fit was found using Eq. (4).

[0050] It should be noted that alternatives to Eq. (4) are possible.

[0051] Model -predicted variables that may be measured in the laboratory. V : the volume of the particulate-laden fluid that has passed through the perforation (m3), Vpthe volume of theparticulates that has passed through the perforation (m3), Vbthe volume of the particulate-laden fluid that has passed through the perforation at the time of bridging (m3), Vp: the volume of particulates that has passed through the perforation at the time of bridging (m3), Mp: the mass, of particulates that has passed through the perforation at the time of bridging (kg), qperf : the volumetric flow rate through the perforation (m3 / s), cpthe volume fraction of particulates in the fluid (m3 / m3), dpthe particulates size, dperf the perforation diameter, rperp the perforation radius, pp-. the density of the particulates (kg / m3), / ? : the volume of particulates required to bridge at low values of qperf, o : a reference volumetric flow rate through the perforation (m3 / s), ah. : the value of a at very low values of qperf (dimensionless), ahr: the value of a at very large values of qperf (dimensionless).

[0052] The experimentally calibrated model may be used to predict when bridging occurs in any of the wellbore’s perforations during a wellbore treatment design. This can be done by using a wellbore treatment simulator, that tracks the flowrate r / ^ / in each perforation at all times during the injection. Thus, the placement simulator can predict when the volume of particulate FPinjected in any perforation has reached or exceeded the bridging volume Vpfor this perforation. Consequently, the combination of the placement simulator and the experimentally calibrated model can be used to predict how much diversion is occurring, during the treatment. This is achieved by predicting the effect of bridging on the perforation injectivity. For predicting the perforation injectivity when it is bridged, a model such as the one proposed in Understanding Diversion with a Novel Fiber-Laden Acid System for Matrix Acidizing ofCarbonate Formations (SPE-134495-MS) SPE Annual Technical Conference and Exhibition,2010, Cohen, C. E. ; Tardy, P. M. J. ; Lesko, T. ; Lecerf, B. ; Pavlova, S. ; Voropaev, S. ;McHaweh, A may be used.

[0053] FIG. 7 illustrates a flow diagram of a process 120 for generating a bridging volume output and / or fluid diversion output, in accordance with embodiments of the present disclosure. In some embodiments, the process 120 may be performed by the well control system and / or or any suitable control system (e.g., having one or more processor that executed instructions stored in memory). In general, the process 120, at block 122, includes determining one or more bridging volumes. For example, block 122, may include performing one or more laboratory bridging experiments to performing laboratory bridging experiments determining Vpor Vb{or Mp with the range of <5, qperf, cpvalues to be thought relevant for the treatment to be pumped in the well of interest and with the particulate-laden fluid in consideration.

[0054] At block 124, the process 120 includes adjusting model parameters based on the one or more bridging volumes. For example, block 124 may include adjusting the model parameters, e.g., / 3 , n, q0, cp, aLr. ahrfor Eq. (1 )-(4) to obtain a satisfactory match (e.g., with a threshold error, of 1% or less, 2% or less, 3% or less, 5% or less, 10% or less) between the model’s prediction of Vbor Vpor Mp, (depending on what is the easiest to determine experimentally) and the values determined experimentally.

[0055] At block 126, the process 120 includes generating a bridging volume output. The bridging volume output may be a control signal, alert, or otherwise that indicates bridging and diversion at the wellbore score. For example, block 126 may include, for each perforation of the well in consideration, associate a bridging model (e.g., Eqs. ( 1 )-(4)) based on the value of 8 for this perforation. Then, the process 120 may include simulating the placement of thetreatment using a simulator. The simulator may determine the volume of fluids and particulates and their flowrate through each perforation and during different time periods. In turn, the process includes monitoring each the simulated Vbor Vp or Mb, for the perforations (e.g., each perforation). Then, the process 120 may include determining a perforation is bridged when one of the simulated volumes exceeds or is below a threshold. For example, the process 120 may include determining that the perforation is bridged when Vp <or Vb< V. Accordingly, the process 120 may include adjusting (e.g., increasing or decreasing) the perforation injectivity (e.g., injectivity flow rate) for a bridged perforation. For example, the bridging volume output may be a control signal or includes instructions to adjust one or more perforation injectivities. For example, the bridging volume output may cause the pump unit 64 to deliver (e.g., injecting) a first amount of fluid to a first perforation. At least in some instances, multiple perforations may be coupled. As such, delivering the first amount of fluid may affect the wellbore pressure and / or total flow rate in other perforations (e.g., in the whole well). The simulator may be updated with the new injectivities when they change. In some embodiments, block 126 may be repeated starting with simulating the placement of the treatment using the simulator.

[0056] For predicting the perforation injectivity when it is bridged, a model may be used employing the concept of “skin” to quantify the flow resistance exerted by the accumulation of the particulates in the perforations and remains valid up to the point where the perforation is filled. The skin scl2obtained by filling the perforations after bridging is the sum of two subskins.SC12 ~SC1 +SC2 (5)where scl: the skin achieved by filling the part of the perforation in contact with the formation. sc2: the skin achieved by filling the part of the perforation in contact with the casing and cement between formation and casing.

[0057] To further illustrate the embodiments disclosed herein, FIG. 8 shows an example of a model system 140 that may be used to determine a bridging volume. In general, the model system 140 includes a chamber having multiple perforations extending from the chamber. As described herein, the volume of fluid flowing along the one or more perforations may be used to determine the bridging volume. As a plug accumulates at the perforation entrance (e.g., where the perforation is coupled to the chamber), a skin may form. The skins are illustrated in FIG. 9. However, the plug accumulation may continue around the perforation entrance once it is filled. Large scale flow loop experiments performed with a 6” PVC clear pipe equipped with multiple 0.25” perforations have been performed to test the validity of the present bridging model.Pictures of the plug extending at the perforation entrance into the wellbore can be seen in FIG. 9.

[0058] Assuming a spherical flow field as in the configuration illustrated in FIG. 9, the following relationship can be obtained by integrating Darcy’s law for the hemisphere.where Apc3: the pressure drop across the plug (e.g., a hemispherical particulates cake) (Pa), rc3: the hemisphere radius (m), shown in FIG. 9, kcthe plug permeability (m2).

[0059] In the case of radial flow in the formation around the wellbore, the expression for the skin associated with plugs may be represented as:where sperj- number of perforations per unit length of wellbore (1 / m), and k : the permeability of the formation around the perforation (m2).

[0060] the total skin scdue to the plug becomes:

[0061] This skin formula can be implemented in treatment placement simulators to complement any existing skin predicting the effect of filling perforations with particulates.

[0062] Technical effects of the present disclosure include a model that utilizes injection rate, which is not used in conventional models. Further, the disclosed techniques provide more accurate techniques for determining an amount of diverter. The disclosed model (e.g., diversion model) may utilize calibration based on different validation techniques (flow loop experiment, yard test experiments, field treatments). The disclosed model may be a physical model that is used to predict particulate as compared to conventional techniques that may use an algorithm to calculate the volume of diverter volume pill based on the heterogeneity of the rock parameters, sequentially through the treatment. Conventional techniques may not utilize predictive modeling aspect, and instead the conventional techniques may utilize a method to choose the mix of different particle sizes to achieve optimum diversion.

[0063] The specific embodiments described above have been illustrated by way of example, and it should be understood that these embodiments may be susceptible to various modificationsand alternative forms. It should be further understood that the claims are not intended to be limited to the particular forms disclosed, but rather to cover all modifications, equivalents, and alternatives falling within the spirit and scope of this disclosure.

Claims

CLAIMS1. A method, comprising: utilizing a physics based empirical model to predict fluid diversion away from one or more constrictions of a fluid diverter system disposed within a wellbore based on an injection rate, concentration of diverter material, particulate type ratios of particulate types in the fluid diverter system, carrier fluid rheology, or a combination thereof; generating an output based on the predicted fluid diversion.

2. The method of claim 1, wherein the one or more constrictions comprise perforations, wormholes, induced fractures, natural fractures, flow control valves, intelligent completion devices, other downhole valves, other completion elements such as packers, or a combination thereof.

3. The method of claim 1, comprising determining a particulate skin including skin of a plug in a wellbore region connected with a perforation tunnel or to a wormhole entrance; and generating the output based on the determined particulate skin.

4. The method of claim 1, wherein if the diverter material is degradable, the physics based empirical model encapsulates a degradation effect of the diverter material as a function of temperature, pH, and exposure time, and its impact on the fluid diversion.

5. The method of claim 1, wherein utilizing the physics based empirical model comprises using experimental and field treatment data to calibrate tuning parameters in the physics based empirical model.

6. The method of claim 1, wherein measurement techniques such as real time telemetry, production logs, flow quantification logs or distributed sensing results are utilized to calibrate tuning parameters in the physics based empirical model.

7. The method of claim 5, wherein utilizing the physics based empirical model comprises adjusting the tuning parameters in the physics based empirical model using data analytics and machine learning methods.

8. The method of claim 1, wherein utilizing the physics based empirical model comprises optimizing ratios of different particulate types within the fluid diverter system, such as fibers, beads, flakes, or a combination thereof, through analysis of a bridging volume prediction.

9. The method of claim 1, comprising implementing the output to divert fluids in geothermal wells to improve heat recovery from geothermal reservoirs.

10. The method of claim 1, wherein the particulate types comprise various particulate sizes, various particulate shapes, or a combination thereof.

11. A system, comprising: a control system comprising one or more processors, wherein the control system is configured to: determine one or more bridging volumes formed within a wellbore; adjust one or more model parameters of a model based on the one or more bridging volumes, wherein the model represents a fluid diverter system based on an injection rate, concentration of diverter material, particulate type ratios of particulate types in the fluid diverter system, carrier fluid rheology, or a combination thereof, and wherein the model is stored in a storage component that is accessible by the control system; and generate a bridging volume output based on the one or more adjusted model parameters.

12. The system of claim 11, wherein the bridging volume output is configured to generate an alert indicating an occurrence of bridging.

13. The system of claim 11, wherein the bridging volume output comprises a control signal configured to adjust a perforation injectivity.

14. The system of claim 11, wherein the control system is configured to generate the bridging volume output by: determining a volume of fluids, particulates, or both, flowing through a perforation during a time period;determining the perforation is bridged when a volume of fluids, a volume or particulates, or both, exceeds or is below a threshold; and generating the bridging volume output based on the determination that the perforation is bridged.

15. The system of claim 11, wherein the particulate types comprise various particulate sizes, various particulate shapes, or a combination thereof.

16. A method, comprising: determining one or more bridging volumes with a wellbore perforation; adjusting one or more model parameters of a model based on the one or more bridging volumes, wherein the model represents a fluid diverter system based on an injection rate, concentration of diverter material, particulate type ratios of particulate types in the fluid diverter system, carrier fluid rheology, or a combination thereof; and generating a bridging volume output based on the one or more adjusted model parameters.

17. The method of claim 16, wherein generating the bridging volume output comprises: determining a volume of fluids, particulates, or both, flowing through the wellbore perforation during a time period; determining the wellbore perforation is bridged when a volume of fluids, a volume or particulates, or both, exceeds or is below a threshold; andgenerating the bridging volume output based on the determination that the wellbore perforation is bridged.

18. The method of claim 16, further comprising adjusting a perforation injectivity based on the bridging volume output.

19. The method of claim 16, wherein the model comprises an empirical particular bridging model and a skin model.

20. The method of claim 16, wherein adjusting the one or more model parameters comprises: quantifying a flow resistance exerted by the accumulation of the particulates types in the fluid diverter system; determining a particulate skin the particulate types based on the flow resistance; and adjusting the one or more model parameters based on the determined particulate skin.

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